How to improve neural network training against a large data set of points with varying magnitude
I think there is no special method for training the neural network in large datasets. But I can add some suggestion for you:

1) Use the convolutional neural network for this dataset.

2) You can use huber loss instead of squared loss and see what happens.

3) See if you have enough small magnitude training data.

Also, please define your problem in more detail (like what those images represent and what you want to predict, what are the features etc).